Last night, Democratic mayoral candidate called for Schools Chancellor Joel Klein to be fired.

But at a debate in midtown this morning, the four Democrats running to replace Thompson as city comptroller were split on whether to oust Klein. (Thompson called yesterday for Klein to be fired.)

While David Weprin and John Liu both called for Klein’s removal, David Yassky said “absolutely not,” while Melinda Katz’s nuanced answer left the debate moderator to categorize her as a “no comment.” After the event, she told me she would not remove Klein now, saying that other, more important changes are needed.

Also worth noting was the slight bit of education criticism from Yassky, who is generally considered an ally of Bloomberg and even employs one of his political consultants, Josh Isay of Knickerbocker SKD. When answering the question about Klein, Yassky also took the opportunity to say, “Graduation improvement is overstated; however, it’s real.”

The event was organized by Crain’s, and its editor, Greg David, moderated along with City Hall Bureau Chief David Seifman of the New York Post.

The four Democrats were asked by Seifman if they’d set up a separate office to “monitor City Council spending.” The question was prefaced by the observation that the Council’s system of allocating discretionary funds is currently being probed and has already led to the resignation of one member, Miguel Martinez of Manhattan.

Yassky said yes, and that he’d “go further” than setting up an office to monitor Council spending. He said he’ll continue his call for an “end to virtual all earmarks,” which he did in an op-ed in the New York Post earlier. The upshot, Yassky said was that without haggling over that relatively small pool of money, members could really start “get into the meat” of the $60 billion budget.

Katz said “maybe” another office was needed, but stressed she’d work cooperatively with others to find a solution. She said a solution was need “if for nothing else, simply so that people have faith in their elected officials.”

Liu said he would create a “special unit” to probe that money, but said “to stop with ‘the City Council is shortsighted.’ It’s easy to have headlines about council members giving out member items. The fact of the matter is the no-bid contracts put out by the City Council are a small fraction of the totality of no-bid contracts in the city.”

Weprin said he was unsure if a whole other office was needed, but said he would conduct more audits. Weprin also took a shot at Yassky, saying, “It’s one thing to write an op-ed piece and to criticize them and at the same time, take them and use them for local groups in his district.”

Later, Yassky said it would be “irresponsible” for his constituents not to get available funding because of his objection to the overall system.